Group #21426146 — subgroups

Subgroups — #21426146

Order 7552.

154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273673	C₂	1	2	yes	maximal
2	#16837782	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#16837205	C₂	1	2	yes	maximal
5	C₄×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₃₆	—	2	1	no	—
7	C₂×Dic₂₃₆	C₂²	1	2	yes	—
8	#14273727	—	2	1	no	—
9	#14273673	—	2	4	no	—
10	C₂×C₅₉⋊C₁₆	C₂²	1	2	yes	—
11	C₂×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
12	C₄×Q₈×C₅₉	—	2	1	no	—
13	#107×C₅₉	C₂²	1	1	yes	characteristic
14	#103×C₅₉	—	2	1	no	—
15	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₅₉	—	2	1	no	—
17	C₂×Dic₁₁₈	—	2	2	no	—
18	Q₁₆×C₅₉	—	2	1	no	—
19	Q₁₆×C₅₉	D₄	1	2	yes	—
20	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₅₉	—	2	1	no	—
23	C₄⋊C₄×C₅₉	—	4	1	no	—
24	C₄²×C₅₉	—	4	1	no	—
25	C₄²×C₅₉	D₄	1	1	yes	characteristic
26	C₄⋊Dic₅₉	—	4	1	no	—
27	C₄⋊Dic₅₉	—	4	1	no	—
28	Dic₂₃₆	—	2	2	no	—
29	Dic₂₃₆	—	2	2	no	—
30	Dic₂₃₆	—	4	2	no	—
31	C₅₉⋊C₁₆	—	2	2	no	—
32	Q₈×C₅₉	—	2	2	no	—
33	Q₈×C₅₉	—	4	1	no	—
34	C₂×C₄×C₅₉	—	4	1	no	—
35	C₂×C₄×C₅₉	—	4	1	no	—
36	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
37	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₅₉	—	4	2	no	—
40	Dic₁₁₈	—	4	2	no	—
41	Dic₁₁₈	—	4	2	no	—
42	C₈×C₅₉	—	2	1	no	—
43	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
44	C₈×C₅₉	#41	1	1	yes	characteristic
45	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
46	C₄×C₅₉	—	2	1	no	—
47	C₄×C₅₉	—	4	2	no	—
48	C₄×C₅₉	—	8	1	no	—
49	C₄×C₅₉	Q₃₂	1	2	yes	complemented
50	C₄×C₅₉	#121	1	1	yes	characteristic
51	C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
52	Dic₅₉	—	8	2	no	—
53	#2209	—	59	1	no	maximal, Sylow
54	C₂×C₅₉	#459	1	1	yes	characteristic
55	C₂×C₅₉	C₂×Q₃₂	1	1	yes	characteristic
56	C₂×C₅₉	#510	1	1	yes	characteristic
57	C₂×Q₃₂	—	59	2	no	—
58	#494	—	59	1	no	—
59	C₄×Q₁₆	D₅₉	1	1	yes	characteristic
60	C₄⋊C₁₆	—	59	1	no	—
61	#358	—	59	2	no	—
62	C₅₉	#2209	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	59	2	no	—
64	C₂×Q₁₆	—	118	1	no	—
65	C₂×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
66	C₄⋊Q₈	—	118	1	no	—
67	C₄×Q₈	—	2	1	no	—
68	Q₃₂	—	118	4	no	—
69	C₂×C₁₆	—	59	2	no	—
70	#107	C₂×D₅₉	1	1	yes	characteristic
71	#103	—	2	1	no	—
72	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
73	C₂×Q₈	—	2	1	no	—
74	C₂×Q₈	—	118	2	no	—
75	Q₁₆	—	2	1	no	—
76	Q₁₆	—	118	2	no	—
77	Q₁₆	—	118	2	no	—
78	Q₁₆	—	236	2	no	—
79	Q₁₆	D₂₃₆	1	2	yes	—
80	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
81	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
82	C₄⋊C₄	—	2	1	no	—
83	C₄⋊C₄	—	4	1	no	—
84	C₄⋊C₄	—	236	1	no	—
85	C₄⋊C₄	—	236	1	no	—
86	C₄²	—	4	1	no	—
87	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
88	C₁₆	—	118	2	no	—
89	Q₈	—	2	2	no	—
90	Q₈	—	4	1	no	—
91	Q₈	—	236	2	no	—
92	Q₈	—	236	2	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	236	2	no	—
96	C₂×C₄	#11745669	1	1	yes	characteristic
97	C₂×C₄	#11745669	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	C₂×D₂₃₆	1	1	yes	characteristic
101	C₈	#11745685	1	1	yes	characteristic
102	C₂²	C₂×#11745669	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	4	2	no	—
105	C₄	—	8	1	no	—
106	C₄	—	472	2	no	—
107	C₄	#14273673	1	2	yes	complemented
108	C₄	#14273701	1	1	yes	characteristic
109	C₄	#14273752	1	1	yes	characteristic
110	C₂	#16837597	1	1	yes	characteristic
111	C₂	C₂×#14273673	1	1	yes	characteristic
112	C₂	#16837842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273673

C₂

yes

maximal

#16837782

C₂

yes

maximal, characteristic

C₄⋊(C₅₉⋊C₁₆)

C₂

yes

maximal, characteristic

#16837205

C₂

yes

maximal

C₄×Q₁₆×C₅₉

C₂

yes

maximal, characteristic

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

C₂²

yes

—

#14273727

—

#14273673

—

C₂×C₅₉⋊C₁₆

C₂²

yes

—

C₂×Q₁₆×C₅₉

C₂²

yes

characteristic

C₄×Q₈×C₅₉

—

#107×C₅₉

C₂²

yes

characteristic

#103×C₅₉

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

—

C₂×Dic₁₁₈

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

D₄

yes

—

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

D₄

yes

characteristic

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

C₅₉⋊C₁₆

—

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

D₈

yes

characteristic

C₂×C₄×C₅₉

D₈

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

#41

yes

characteristic

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

Q₃₂

yes

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

C₂×Q₃₂

yes

characteristic

C₂×C₅₉

#510

yes

characteristic

C₂×Q₃₂

—

#494

—

C₄×Q₁₆

D₅₉

yes

characteristic

C₄⋊C₁₆

—

#358

—

C₅₉

#2209

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

118

—

C₂×Q₁₆

C₂×D₅₉

yes

characteristic

C₄⋊Q₈

—

118

—

C₄×Q₈

—

Q₃₂

—

118

—

C₂×C₁₆

—

#107

C₂×D₅₉

yes

characteristic

#103

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

118

—

Q₁₆

—

Q₁₆

—

118

—

Q₁₆

—

118

—

Q₁₆

—

236

—

Q₁₆

D₂₃₆

yes

—

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

236

—

C₄⋊C₄

—

236

—

C₄²

—

C₄²

C₂²⋊D₅₉

yes

characteristic

C₁₆

—

118

—

Q₈

—

Q₈

—

Q₈

—

236

—

Q₈

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

C₈

—

100

C₈

C₂×D₂₃₆

yes

characteristic

101

C₈

#11745685

yes

characteristic

102

C₂²

C₂×#11745669

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

472

—

107

C₄

#14273673

yes

complemented

108

C₄

#14273701

yes

characteristic

109

C₄

#14273752

yes

characteristic

110

C₂

#16837597

yes

characteristic

111

C₂

C₂×#14273673

yes

characteristic

112

C₂

#16837842

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11745669
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₄×Q₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	C₄×Q₁₆	D₅₉
hypocenter	C₅₉	#2209
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂²

C₂×#11745669

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₄×Q₁₆×C₅₉

C₂

socle

C₂²×C₅₉

C₂×D₈

hypercenter

C₄×Q₁₆

D₅₉

hypocenter

C₅₉

#2209

LCS

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

N	H ≅ G/N	type
49. C₄×C₅₉	Q₃₂	semidirect
62. C₅₉	#2209	semidirect
107. C₄	#14273673	semidirect

H ≅ G/N

type

49. C₄×C₅₉

Q₃₂

semidirect

62. C₅₉

#2209

semidirect

107. C₄

#14273673

semidirect

Subgroups — #21426146

Conjugacy classes of subgroups

Complements